QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems
Alberto Mercurio, Yi-Te Huang, Li-Xun Cai, Yueh-Nan Chen, Vincenzo Savona, Franco Nori
Abstract
We present <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="monospace">Q</mml:mi><mml:mi mathvariant="monospace">u</mml:mi><mml:mi mathvariant="monospace">a</mml:mi><mml:mi mathvariant="monospace">n</mml:mi><mml:mi mathvariant="monospace">t</mml:mi><mml:mi mathvariant="monospace">u</mml:mi><mml:mi mathvariant="monospace">m</mml:mi><mml:mi mathvariant="monospace">T</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">l</mml:mi><mml:mi mathvariant="monospace">b</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">x</mml:mi><mml:mo mathvariant="monospace">.</mml:mo><mml:mi mathvariant="monospace">j</mml:mi><mml:mi mathvariant="monospace">l</mml:mi></mml:mrow></mml:math>, an open-source Julia package for simulating open quantum systems. Designed with a syntax familiar to users of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="monospace">Q</mml:mi><mml:mi mathvariant="monospace">u</mml:mi><mml:mi mathvariant="monospace">T</mml:mi><mml:mi mathvariant="monospace">i</mml:mi><mml:mi mathvariant="monospace">P</mml:mi></mml:mrow></mml:math> (Quantum Toolbox in Python), it harnesses Julia's high-performance ecosystem to deliver fast and scalable simulations. The package includes a suite of time-evolution solvers supporting distributed computing and GPU acceleration, enabling efficient simulation of large-scale quantum systems. We also show how <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="monospace">Q</mml:mi><mml:mi mathvariant="monospace">u</mml:mi><mml:mi mathvariant="monospace">a</mml:mi><mml:mi mathvariant="monospace">n</mml:mi><mml:mi mathvariant="monospace">t</mml:mi><mml:mi mathvariant="monospace">u</mml:mi><mml:mi mathvariant="monospace">m</mml:mi><mml:mi mathvariant="monospace">T</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">l</mml:mi><mml:mi mathvariant="monospace">b</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">x</mml:mi><mml:mo mathvariant="monospace">.</mml:mo><mml:mi mathvariant="monospace">j</mml:mi><mml:mi mathvariant="monospace">l</mml:mi></mml:mrow></mml:math> can integrate with automatic differentiation tools, making it well-suited for gradient-based optimization tasks such as quantum optimal control. Benchmark comparisons demonstrate substantial performance gains over existing frameworks. With its flexible design and computational efficiency, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="monospace">Q</mml:mi><mml:mi mathvariant="monospace">u</mml:mi><mml:mi mathvariant="monospace">a</mml:mi><mml:mi mathvariant="monospace">n</mml:mi><mml:mi mathvariant="monospace">t</mml:mi><mml:mi mathvariant="monospace">u</mml:mi><mml:mi mathvariant="monospace">m</mml:mi><mml:mi mathvariant="monospace">T</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">l</mml:mi><mml:mi mathvariant="monospace">b</mml:mi><mml:mi mathvariant="monospace">o</mml:mi><mml:mi mathvariant="monospace">x</mml:mi><mml:mo mathvariant="monospace">.</mml:mo><mml:mi mathvariant="monospace">j</mml:mi><mml:mi mathvariant="monospace">l</mml:mi></mml:mrow></mml:math> serves as a powerful tool for both theoretical studies and practical applications in quantum science.